Well-posedness of the Stokes-transport system in bounded domains and in the infinite strip

2021 ◽  
Author(s):  
Antoine Leblond
Keyword(s):  
Transport System ◽  
Infinite Strip ◽  
Well Posedness ◽  
Bounded Domains ◽  
Stokes Transport

scholarly journals On the cubic NLS on 3D compact domains

2013 ◽  
Vol 13 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Fabrice Planchon
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Schrodinger Equation ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Dirichlet Boundary Conditions ◽  
Well Posedness ◽  
Bounded Domains ◽  
Bilinear Estimates

AbstractWe prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the ${ \mathbb{R} }^{3} $ case, while on bounded domains they match the generic boundaryless manifold case. We obtain, as an application, global well-posedness for the defocusing cubic NLS for data in ${ H}_{0}^{s} (\Omega )$, $1\lt s\leq 3$, with $\Omega $ any bounded domain with smooth boundary.

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